The invention is based on an apparatus as generically defined hereinafter. When air flow rate meters are used in the intake tube of internal combustion engines, the problem arises that in certain engine operating ranges, very severe pulsations in the aspirated air cause a falsification of the measurement signal, and as a result of this fact that reversals in the flow direction occur but are not recognized as such by the air flow rate measuring device. It has therefore been suggested previously that the flow measurement be interrupted when the pulsation amplitudes are very high; however, this is unsatisfactory because it does not bring about a correction of or compensation for the pulsation error.